 |
| |
|
This case is designed to assess the input impedance of a wire dipole in free space. Results are validated against tabulated King-Middleton second order admittance values for linear dipoles[1,2].
In FDTD thin wires can rarely be discretised at the resolution of their radius and so it is necessary to apply a method to treat them within cells that are many times larger. The method used in Celia is that of Umashankar et. al.[3] This method involves the application of the contour path integration method to couple the wire to the cell.
This method has been proven over many years, although experience[4] shows that it is more accurate for fat wires than for thin ones. Results are shown below that show the drive point impedance of 2 dipoles of differing radii. Values of W of 10 and 20 (where W =2ln(L/a) ) are considered. Each dipole was of length 41 cells, physical length 0.2m, and the mesh boundary was located everywhere 5 cells from the wire. A PML of 6 cells thickness was used as the RBC. The feed used is the balanced transmission line feed reported in Bourgeois and Smith[5].
Within Celia the wire method of Umashankar has been modified using an empirical correction to improve the accuracy of the wire method. This correction gives more accurate results for the coupling of the wire to the FDTD cells. The difference is particularly clear for thin dipoles where the corrected results correspond well with the King-Middleton results. This exercise is a particularly stringent test of the RBC, which must perform well to get accurate results for the low frequency resonances in the dipole. In particular, the input impedance at the first resonance is around 73ohms for a dipole in free space, the accuracy of this value is an indication of how well the RBC is behaving.
The plots show results computed using Celia compared to the King-Middleton results as a function of k/a, where k is the wave number. FDTD results are shown for the standard Umashankar method and the corrected method implemented in Celia. The computed input resistance at the first resonance is 71W in both cases.
1 Collin R E, Zucker F J
'Antenna Theory'
McGraw-Hill, New York, 1968
2 King R W P
'Tables of Antenna Characteristics'
Plenum Press, New York, 1971
3 Umashankar K, Taflove A, Becker B
'Calculation and experimental validation of induced currents on coupled wires
in an arbitrary shaped cavity'
IEEE Transactions on Antennas and Propagation
Vol 35, Nov 95, pp 1248-1257
4 Hockanson D M, Drewniak J L, Hubing T H, Van Doren T P
'FDTD Modelling of Common Mode Radiation from Cables'
IEEE Transactions on EMC
Vol 38, No. 3, Aug 96, pp 376-386
5 Bourgeois J M, Smith G S
'A Fully Three-Dimensional Simulation of Ground-Penetrating Radar: FDTD Theory
Compared with Experiment'
IEEE Transactions on Geoscience and Remote Sensing
Vol 34, No 1, Sept 1996, p36